We spent 7 days in June -July this year. Never seems like enough time but we had a VERY relaxing vacation! Of course I love the whole resort and could easily spend two weeks there! 3 full days in July you will be busy! If you go gung ho commando you can probably get a lot in but I much prefer a more leisurely pace.
Yes, if you do things right. Most people look at DLR as a leisurely vacation. So they sleep in and show up to the park gates 1-2 hours after the park opens. If you visit that way it will make it harder to "do it all" in three days, which is not to say you will not have a fun time. If you get to the parks early, start grabbing FastPasses right away, you can pretty much do it all including the shows.
I think it is possible. Arrive early!!!! I also would park hop. Usually it doesn't take us all day for DCA. 1/2-1 day at DCA, 2-2 1/2 days at DL and you should do most of what you want. Even a few times.
We just returned from a trip 11/21-11/25. We went to Disneyland the evening of 11/21, evening of 11/22 and all day 11/24. DCA for 1/2 day on 11/22 which was more than enough time as my dd (and me) don't like the rollercoasters or scarier rides.